Mayor Bloomberg is pushing River forward with a proposal that would extend the No. 7 subway line from the West Side of Manhattan to New Jersey. The proposal would call for a new Hudson River tunnel connecting the subway to an NJ Transit rail hub in Secaucus. With an estimated cost of $10 billion, the project would take a decade to complete. Photo: Ellis Kaplan

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Mayor Bloomberg is pushing forward with a proposal to extend the No. 7 train to New Jersey and get the project locked in before he leaves City Hall in two years, The Post has learned.

Although noncommittal in public, Hizzoner is now a fan of the concept and is looking to announce the next planning steps in the coming months, sources said.

Bloomberg would then be able to go public with a formal proposal by the end of 2012, in a bid to get the New Jersey-bound No. 7 tunnel on track by the close of his third term, Dec. 31, 2013.

“This is a really good project,” one source involved in the planning told The Post. “The mayor wants this. And it’s a heck of a lot better” than the previous tunnel project killed last year by New Jersey Gov. Chris Christie.

Bloomberg’s enthusiasm grew in recent weeks after he saw the findings of a preliminary feasibility study from engineering firm Parsons Brinckerhoff.

The city paid $250,000 for that analysis, which lays out a plan for a tunnel that would connect the Hudson Yards on the far West Side to Secaucus, NJ. The subway line would terminate at the Secaucus Junction rail station along the New Jersey Turnpike.

Analysts believe the project would spur development along the West Side and relieve crowding on the NJ Transit lines and at Manhattan’s Penn Station.

The cross-Hudson tunnel would connect to the 7 train, which is being extended from Time Square to a new terminal at 11th Avenue and 34th Street. The current project will be completed in 14 months.

The next steps in the process are a full business plan and environmental-impact study, which have not yet been commissioned.

During his weekly radio appearance on WOR Friday, Bloomberg didn’t reveal his enthusiasm for the project, saying only, “If there’s money for it and it makes sense, I’d certainly support it.”

But yesterday, Bloomberg spokeswoman Julie Wood sounded a more optimistic note: “Since we began exploring this idea, we continue to think it has a lot of potential as a way to cost-effectively improve regional transportation and also create thousands of jobs.”

Officials in the Christie administration and the Port Authority are working with City Hall on the No. 7 concept, but insist that the mayor take the lead.

Christie spokesman Michael Drewniak said yesterday, “We have been intrigued all along by this as a potential alternative.”

A year ago, Bloomberg was reluctant to pony up any dough when Christie killed a New York-New Jersey tunnel project called ARC, or Access to the Region’s Core. That project called for a new tunnel for NJ Transit commuter trains to be built from Secaucus to Herald Square.

Christie said ARC’s design was flawed, and its price tag was no longer reasonable after ballooning to a range of $11 billion to $14 billion — up from $8.7 billion.

Early estimates say a No. 7 tunnel could be built for less than $10 billion, a sum that would be split among the city, the PA and New Jersey. Officials are also planning to hit up the feds for cash.

Extending the No. 7 to New Jersey would quickly become a key talking point in the mayor’s legacy.

Bloomberg has envisioned that the 7 train extension would spark a new building boom of high-rise office towers in the Hudson Yards area — development he’s banking on to help repay bonds that were sold to pay for the project.